Tuesday, May 31, 2005
... /////

We returned from a seminar at MIT. Ashoke Sen was checking the entropy of heterotic black holes. At weak coupling, such an object has to look like an excited heterotic string. A heterotic string is made of two types of important excitations:

the left wing

the right wing

Note that both wings are important. The left wing gives it its potential instability and tachyons and ugliness. The right wing, on the other hand, gives the heterotic string its supersymmetry, beauty, and stability. ;-)

The number of left-moving and right-moving excitations must match. If you imagine a compactification on a circle - times a 5-torus - you may still obtain supersymmetric states that satisfy

N_R = 0, N_L = n.w+1

where "n" is the momentum along the special circle and "w" is the winding. Note that the difference between "N_L" and "N_R" is determined by the level-matching conditions, and in the presence of momenta and winding, it is not zero but rather "n.w+1". There are no right-moving excitations, and because supersymmetry is only carried by the right-movers, it is not broken.

Sunday, May 29, 2005
... /////

My feelings about the result are mostly positive, but still mixed a bit. France, one of the champions of European integration, rejected the proposed constitution. Most of the "NON" votes had a "wrong" reason, although there have been many reasons behind the "NON" votes, but I completely respect all of them, much like the arguments behind the "OUI" votes. It is totally obvious that the EU constitution would further diminish the chances of French farmers and workers. The Eastern European competition is tough already today, and most French citizens have probably figured out that the further integration of the EU, according to the constitution, would also mean a further wave of uniformization of the continent. In other words, the economic standards of France and the new member states would continue to converge. France has been a payer in the EU budget, and this also implies that the results had to be different from Spain, for example.

Many dissent socialists voted against the constitution because it was not social and environmental enough - the text seemed as an example of the Anglo-Saxon influence that is intended to destroy the French welfare state. Well, that's ironic because the same constitution may fail in Britain or elsewhere because of the opposite reason. But yes, I agree that the text of the constitution has a neo-liberal, free market flavor. The text tried to define too many things. Many French voters agreed with me that the economic principles should simply not be written down in the constitution - such things belong to the programs of political parties and should not be defined in a long-lasting text. More generally, the constitution is just too long. If it were 10 times as short, it would be more reasonable.

The unpopular French prime minister Raffarin is gonna be fired tomorrow. The Dutch are likely to vote against the treaty on Wednesday, too. Some unusual politicians, such as Juncker from Luxembourg, will propose that the EU constitution continues without France. Others will propose another referendum in France. Most mainstream people will agree that the constitution has been stopped cold in its tracks.

This looks like a pretty interesting and bizarre story. A few weeks ago, a mysterious man in a soaking wet suit was found in Britain. He does not communicate with anyone and is extremely shy. After several attempts to initiate an interaction, he drew a nice picture of a piano, and once they allowed him to play, he was playing classical pieces for 4 hours from memory. An accomplished amateur, they say.

The British could not find out who he was. The best hint they received was a statement of a Polish mime who illegally works in the streets of Rome. This Pole claimed that the Piano Man was his former colleague from Nice - the French musician allegedly called Steven Villa Masson. A week ago, this source and his piece of information apparently turned out to be good enough for CNN and the theory has been announced by CNN as well as tens of other sources as the final answer to the mystery.

Well, one may feel a bit unsatisfied with this kind of an answer. Don't get me wrong - I have absolutely nothing against the Polish street mimes currently working in Italy. :-) But still, the name "Steven Villa Masson" does not seem to be terribly official as far as I can say. Moreover, Masson has been tracked down in Nice. Today, The Independent offered something better.

They were contacted by Mr. Klaudius Kryšpín [Clow-dee-oos Krish-peen], the drummer from the most famous Czech hard rock band of the 1980s and 1990s, namely Pražský výběr (Prague Selection, [Prash-skee Vee-b'er]). Kryšpín emigrated to Australia in 1988 and returned to Prague after the Communism collapsed. If you want to hear how Pražský výběr sounds, you should be satisfied with this very low quality file - my version of "Pražákům těm je tu hej" (The natives are doing fine, they can't get lost here in Prague).

What did Kryšpín say? He claims that the Piano Man is Mr. Tomáš Strnad [Taw-mash Stir-nut], his colleague from Ropotamo, an anti-communist teenager band from the 1980s that was immitating (equally anti-Communist) Pražský výběr. Strnad was able to play the piano for hours from memory and attempted to become a classical piano player after 1989 which did not work out. Kryšpín, on the other hand, joined the "real" Pražský výběr itself. The Independent argues that a picture of Strnad from 1983, as shown them by Kryšpín, has a striking resemblance to the Piano Man. If this is true, the man on the picture on the CNN page above must be nearly 40 unless some extraordinary redshift or time dilation changes the proper time! Kryšpín also argues that he knows a birthmark that could identify the Piano Man as Tomáš Strnad.

Kryšpín has not seen Strnad for 9 years. He knows that Strnad did not really get along with his family and 3 years ago he was begging. Kryšpín's brother Richard - the guitarist of their band - now works in Columbus, Ohio as a computer analyst. He also confirms that the Piano Man looks like Strnad, and mentions that Strnad used to have mental problems.

Michael Kocab - the well-known singer of Pražský výběr who also became a politician for a couple of years following the 1989 Velvet Revolution - also said that Strnad may be the Piano Man. Kocab also claims that he met Strnad roughly 2 months ago at a gas station at the outskirts or Prague. Strnad seemed very confused and he mentioned that he would go abroad, most likely to the U.S., to build his career. There is a subtlety however: Kocab argues that this moment when he met Strnad was on April 10th - 3 days after Strnad was officially hospitalized in England.

Thursday, May 26, 2005
... /////

They claim that the usual wisdom about the Hagedorn phase transition is incorrect. The usual wisdom is that the exponential growth of the density of states implies that at temperatures higher than the Hagedorn temperature, the second quantized spacetime partition sum diverges because the Boltzmann factor is not sufficient to suppress the exponential growth of the number of states. Alternatively, the Hagedorn transition can be seen as the appearance of a tachyon in the channel related by modular transformations.

Dienes and Lennek argue that this widely believed argument is wrong.

In the UV picture, the divergence is wrong in string theory, they say, because it effectively leads to you to treat string theory as field theory with many fields, which means that the one-loop integrals over "tau" are made over "Im(tau)" being positive and "Re(tau)" smaller than one-half. The correct stringy integral involves the fundamental domain of the modular group "SL(2,Z)", and if this domain is used, the divergence at the (old) Hagedorn point disappears, they claim.

In the IR picture based on the existence of tachyon, they note that the tachyon is actually projected out by the GSO projections, and consequently, it has no physical consequences. The usual Hagedorn phase transition is therefore absent in heterotic string theories and other tachyon-free superstring theories. They affirm that the Hagedorn behavior in type 0 theories, for example, still holds.

They also say that these two interpretations are consistent and related by a modular transformation. In another section of their paper, they propose that the Hagedorn transition in these non-tachyonic theories occurs after all, but at higher temperature than anticipated. The relevant temperature is not derived from a tachyon but rather from proto-gravitons and proto-gravitinos, as they call it. The resulting alternative temperature is universal for all string (heterotic and type II) theories, unlike the conventional Hagedorn temperature where the temperatures differ by factors such as "2" or "2-sqrt(2)". Their new universal Hagedorn temperature equals "a = 1/sqrt(2)" times the temperature that gives you the T-selfdual circumference of the thermal circle. You know that the conventional inverse Hagedorn temperature "beta_H" is not exactly the self-dual circumference under T-duality, and their new one is not either.

Wednesday, May 25, 2005
... /////

Lenny has already used this title for several talks. I won't comment on the summary of the book, but it is very provocative:

The beginning of the 21st Century is a watershed in modern science, a time that will forever change our understanding of the universe, Leonard Susskind, the father of string theory, contends. With this theory, he inspired a generation of physicists who believe that this theory would uniquely predict the physical properties of our universe. Now, decades later, Susskind is revising his theory, saying that it no longer suits our understanding of the universe. In this book he raises the possibility that the Laws of Physics as we know them today are determined by the requirement that intelligent life is possible. In other words, our universe exists because we are here to observe it. THE COSMIC LANDSCAPE will be a paradigm shifting answer to Brian Greene’s bestselling The Elegant Universe.

In the most recent issue of "Scientific American," Steve Giddings and Bernard Carr explain why and how the LHC is conceivably going to produce a lot of tiny black holes and what it means for our knowledge of physics and for our survival:

Tuesday, May 24, 2005
... /////

This text uses Techexplorer to display math formulae. You may download it but I doubt that it is worth the hassle just in order to see a few cheap formulae in this text.

Superstring theory, according to the conventional wisdom, predicts 10 spacetime dimensions. M-theory, its special state, predicts 11. If it describes the real world, 6 or 7 dimensions must be hidden in one way or another. The simplest way to hide them is compactification: the extra 6 or 7 coordinates parameterize a compact shape (a manifold). The simplest compactification is toroidal compactification where you make the coordinates periodic.

Such a treatment preserves all supersymmetries of the original spacetime, and it is not realistic at all. What is the second simplest compact manifold onto which string/M-theory may be compactified? It preserves one half of supersymmetries, it has four real dimensions, and it is the third highest peak in the world after Mount Everest and K2 (as Paul Aspinwall explains in his lecture mentioned at the bottom of this text). How does such a K3 look like? You can either wait for Matt Headrick and Toby Wiseman who are finishing a paper describing the numerical simulations of a particular one-dimensional subclass of K3 surfaces, or you can alternatively look at the following picture:

The animation above was created by Greg Egan and promoted by John Baez. It shows you, once again, how the simplest curved compactification of string theory looks like. Well, not quite. Many K3 surfaces may be written as quartic surfaces in the complex projective space CP3 which in homogeneous coordinates means:

and led by Steve Shenker. We have had many discussions about this topic but I still believe that there are many people (and perhaps readers of this blog) who have interesting ideas that many of us have not heard.

A way to formulate the question is

What is the most underestimated research direction in current theoretical physics?

Note that the revolutions never start from "nothing". Before the first superstring revolution, Green and Schwarz were doing extremely interesting work that was deeply underestimated by the high-energy community. Also, before 1995, there were several directions that were ignored by the string theorists. This includes Paul Townsend, Michael Duff, and others who argued that the 11-dimensional supergravity was relevant for the grand scheme of things.

It may be that today there also exists a research program that will eventually convince the people that it is the right idea that will allow us a new wave of significant progress. The question is:

What is it?

Note that the second superstring revolution had merged the communities of string theorists and supergravity researchers although they had mostly been thought of as separate entities. Should we expect something similar in the future?

Sunday, May 22, 2005
... /////

The physicist Uwe Bergmann is gonna use the gadgets at the Stanford Linear Accelerator Center (SLAC) to decipher Archimedes' notes - created in the 2nd century B.C. and copied in the 10th century A.D. - revealing how he used mechanical devices to derive various mathematical theorems.

Saturday, May 21, 2005
... /////

One of the questions that I was always asking Michael Douglas and others who want to treat the "landscape" anthropically and statistically was whether we know that the number of vacua is finite. This includes our discussions with Michael on sci.physics.strings. My feeling always was that the advocates of the anthropic reasoning always wanted us to assume that the number was finite; I was always convinced it was discretely infinite (countable).

The question about finiteness of the "landscape" is an important question because if someone claims that the probabitility distribution on the space of vacua may be approximated by the uniform distribution in the zeroth approximation (and the exact distribution is simply this number multiplied by another, less important function, or it is even exact?) - an assumption that I've always considered irrational - then an infinite number of vacua presents a big hurdle because there is no uniform distribution on infinite sets.

Why do I think that the assumption is irrational? The numbers like 10^{500} are effectively infinite and a rational argument simply should not break down if this huge number is replaced by the true infinity. If there exists any rule that decides about the probability of different vacua, it must undoubtedly be able to imply that a subclass of 10^{500} vacua - or an infinite subclass for that matter - has a vanishing probabilistic weight. Assuming that this is not possible is equivalent to repeating Zenon's error with Achilles and the turtle: Zenon also believed that Achilles could never catch up with the turtle essentially because the path separating Achilles and the turtle may be divided to infinitely many line intervals.

My personal prejudice is just the opposite one: I believe that the classes of similar vacua with too many elements - i.e. the less predictive ones - will be disfavored when we understand things better at the end. It is roughly because the vacua may be organized as a countable set and the populated classes will only appear at the end (close to the infinity) with a very high "ranking" or "meta-energy" and a small "meta-Maxwell-Boltzmann" statistical weight. This will reflect the desire of the theory to be as predictive as possible. But unlike the statistical counters, I admit that this is a pure prejudice, not a piece of science.

So is the number of vacua finite or infinite? Frankly speaking, the number of vacua has always been infinite. For example, the "AdS4 x S7" supersymmetric backgrounds come as an infinite class parameterized by the integer flux. The only way how we may eliminate some of them is to say that the seven-sphere is really far too large and we only want the backgrounds in which the size of the internal manifold is much smaller than the AdS curvature.

On Wednesday, we reminded ourselves of the whole story of N=2 gauge theory with the SU(2) gauge symmetry - i.e. Seiberg-Witten I - under the leadership of Kirill Saraikin. This nice application of the holomorphy of the prepotential; the known conditions on the allowed behavior around singularities; a known expansion around infinity may be used to reconstruct the low-energy physics exactly. We discussed how much it is known for sure that there are three singularities on the moduli space - of course, the Dijkgraaf-Vafa constructions give us the whole result, including the fact that there are three singularities.

On Thursday, Christopher Beasley who is gonna be at Harvard explained his interesting work with Edward Witten about the non-Abelian localization of Chern-Simons theory. The partition sum was evaluated for a very special subclass of three-dimensional manifolds, the so-called Seifert manifolds, which may be visualized as a U(1) bundle over the genus g Riemann surfaces. Why is it non-Abelian? For their conjecture to work, one must find a group H that acts on the configuration space, and in their case, it is a non-Abelian group.

On Friday, Tasneem Zehra Husain was talking about the SUGRA solutions for M5-branes wrapped on the cycles of various manifolds. She spent some time with introduction - supergravity equations of motion, the conditions for preserved supersymmetry - and the main task is to find out some generally satisfied conditions that hold for the manifolds even after you take the back-reaction into account. The main condition of this sort says that the Hodge dual of the calibration form is closed - i.e. the calibration form is co-closed.

Tuesday, May 17, 2005
... /////

He showed a picture what such a search looks like: a five-year-old boy is searching for something - apparently a needle - in the haystack. In fact, the boy was Burt Ovrut. The picture offers a striking support for the statement that the anthropic landscape is really the anthropic haystack: Nima Arkani-Hamed confirmed this conjecture by pointing out that the landscape looks like a two-dimensional object.

Gary reviewed basics of superstring model building - stabilization of moduli, SUSY breaking that is apparently able to stabilize all the moduli by itself, the black box treatment of SUSY breaking via soft SUSY breaking terms, and the difficulties to obtain the Standard Model in flux compatifications.

Nevertheless his aim was to describe an example: an MSSM from the flux vacuum at the orbifold

His picture how a compactification looks like was an octopus with many throats - such as the MSSM throat, the inflation throat (that also gives us cosmic strings), and so on. Although this separation of different problems may be appealing for many purposes, I generally find such a picture repelling because progress in theoretical physics should reveal new relations between previously unrelated notions instead of simply approving that they are unrelated.

A difficult problem is to obtain a chiral gauge theory. In the context of flux vacua, this goal is achieved by one of two methods:

The type IIB magnetized D-branes are T-dual to intersecting D-branes in type IIA. The type IIA picture is however difficult to deal with because it involves non-Kähler geometry, which is why these people stay in the type IIB context. In the magnetized D-brane framework, the number of chiral generations is essentially counted by the flux. The Pati-Salam models are natural in this context. The dilaton tadpole may be computed as the number of D3-branes but we really want D9-anti-D9 with a bundle that carries the same charges. One must be careful about the Z2-valued K-theoretical charges. They must be cancelled otherwise Witten's anomaly would appear on lower-dimensional D-branes, Gary argued.

How do the fluxes affect the open string moduli? The self-dual fluxes cancel the forces against gravity, via the usual BPS cancellations, while the anti-self-dual ones double it and they stabilize the positions of D-branes. However, the Wilson lines remain flat directions.

In the original article, I have described two talks from the conference at Columbia University. Savdeep Sethi chose a topic - his project with Ben Craps and Erik Verlinde - that was the most appropriate one for a conference about string cosmology. And it was a lot of fun:

The Matrix Big Bang

And because he allowed me to write about it, let's go ahead. It is likely that this article will include some mathematics. If you don't see it, download Techexplorer.

His plan was the following:

Background - for his talk

A background - a very simple background where strings can propagate

Review of BFSS matrix theory

Its holographic description

Sav explained that string theory has been extremely successful in dealing with a certain type of singularities - the timelike singularities such as orbifold and conifold singularities. Some of them even preserve supersymmetry - but most of them respect the finiteness of the effective Newton's gravitational constant.

On the other hand, string theory has so far been unsuccessful to resolve other singularities such as the spacelike singularities near the Big bang and in the middle of the black hole. Sav's description of the source of the problem is that the scattering quanta always "see" an infinite value of Newton's constant at some moment.

There has been a rather long discussion with Dan Kabat and others why there was really any difference in this respect between the spacelike and the timelike singularities, but Dan eventually kind of agreed. Whatever you do, perturbative string theory is guaranteed to fail near the spacelike singularity and a better description is needed.

Of course, Sav's proposed better description is BFSS matrix theory.

But before he got there, he discussed various singular spaces. One of the simplest singular spaces is the Misner space,

where we used the light-like coordinates and identified them via a boost. This orbifold behaves differently in the timelike and spacelike regions of the two-dimensional spacetime: in the timelike region it defines the Milne universe, while the spacelike part of the space is the Rindler space. (Note that the previous sentence contains inline math, and if it displays incorrectly in your browser, let me know.) This Misner space is locally flat, however. What is the simplest background in string theory after the trivial flat space? Well, it is the almost trivial flat space - which means flat space with a slightly non-trivial dilaton.

To make things really simple, we can take the dilaton gradient to be null.

where the parameter Q is fictitious because a boost changes its value. Note that this simple dilaton background does not spoil the equations of motion for the dilaton. It does not change the central charge either. The central charge of your two-dimensional conformal field theory is obtained from the correlator (OPE) of two copies of the stress energy tensor:

where the dots represent less singular terms. The only effect of the linear dilaton on the stress energy tensor is an extra term

where the second term measures the dilaton gradient. It also contributes to the central charge in the OPE

But if the vector V is null, you see that the contribution vanishes because its square is zero. Also, the spectrum of this theory is isomorphic to the spectrum of the trivial theory with constant dilaton. There is an extra term in the Virasoro generator

which can be combined with another term if we replace

Once again, the spectrum of a single string is not really affected by the linear null dilaton.

That's a fine and simple background. But let us study it in the superstringy context, namely type IIA string theory. In that case, we have enough supersymmetry for the metric to be exact and not corrected by quantum corrections. Also, it may be lifted to M-theory. One obtains a non-flat eleven-dimensional geometry in which ten coordinates shrink as we approach the Big Bang while the eleventh coordinate expands. We first rewrite the metric in Einstein frame where it's not flat anymore:

and then we convert it to an eleven-dimensional metric:

This is a cosmologically non-trivial background with a null singularity. Can we understand it? Can we evolve a state at finite time arbitrarily close to the singularity?

How could we ever do it without knowing what M-theory is? We know one definition of M-theory, namely the BFSS matrix model (Banks, Fischler, Shenker, Susskind). Sav reproduced Seiberg's argument why is the matrix model correct.

You want to describe M-theory in 11 dimensions. You artificially compactify the light-like coordinate

As long as R is taken large, physics is reproduced just fine. This null compactification is on the edge of creating deadly time-like curves, and we should rather define it as the limit of nearly null compactifications which are otherwise slightly spacelike. Any such nearly null (but spacelike) compactification can be boosted, using the Lorentz symmetry of M-theory, to a pure and manifestly spacelike compactification of M-theory. Because the identification was almost null, the new spacelike circle will be very short after the boost and we obtain type IIA string theory with coupling that goes to zero. One can prove that the limiting procedure and the energy regime we want to study (finite energies in 11D Planck units in the original picture) decouples all degrees of freedom from the theory except for massless open string states stretched between N D0-branes - well, N D0-branes is what the boost produces out of N units of momenta in the light-like circle "X minus":

Recall that momentum in the light-like direction which becomes the short 11th dimension of type IIA string theory has the perturbative interpretation of the D0-brane charge. Because we want to keep the momentum "p plus" finite and we want to send the light-like radius R to infinity, we must also send N to infinity - and therefore all of physics of M-theory is encoded in the U(N) matrix quantum mechanics which is the dimensional reduction of ten-dimensional Yang-Mills theory to 0+1 dimensions and whose Hamiltonian is (and now I use the tag "autosize='true'" to impress Jacques Distler, hopefully it will work for non-MSIE browsers, too)

Sav also recalled how one obtains matrix string theory - the baby of mine and DVV - by compactifying one more circle in the eleven-dimensional spacetime, thereby producing a matrix model for type IIA string theory which happens to be a maximally supersymmetric Yang-Mills theory in 1+1 dimensions compactified on a spatial circle.

What about Sav's background? He compactified one more background, repeated Seiberg's procedure and obtained matrix string theory defined on the Milne space, the same space that we discussed at the beginning because of other motivations. Surprisingly, the Milne compactification breaks all supersymmetries even though the background we want to describe should have 16 supercharges. I argued that in the large N limit, the full supersymmetry should be recovered in the matrix model and Sav disagreed.

It is not quite clear whether the correct matrix model is just pure Yang-Mills theory or whether excited open string modes remain important. At any rate, Sav's lesson is that we should study open string theories on non-trivial backgrounds because they can tell us - because of open-closed dualities such as matrix theory - non-trivial lessons about the way how quantum gravity resolves cosmological backgrounds.

Monday, May 16, 2005
... /////

Before you install this software, you should close your internet browser. When you re-open this page with Internet Explorer, you should click at "To help protect your security" and you should "Allow the blocked content". One of many advantages of the Techexplorer is that the source may be written not only in MathML, but also directly in TeX or LaTeX. Fine, so let me do several experiments.

First, let us write down a matrix.

Fine, now we should add a nonsensical expression with some different colors:

How quickly can I write down the CP-violating topological term of four-dimensional gravity? It is

That's enough for now. If you want to know how can you write mathematics like the equations above on your web pages, simply click "View/Page Source" and search for the word "embed" (without quotation marks). Paste the "embed" ... "/embed" section onto your web page and edit it: it is self-explanatory and the main thing inside that you will modify is a TeX source.

Saturday, May 14, 2005
... /////

On Friday 13th, Brian Greene and Maulik Parikh at Columbia University, 120th street/Broadway in the New York City, organized the

Fifth addition to the Northeastern conference on string cosmology

and it was a nice and successful event, I think. It's great if such an event is organized by someone who is not just a smart physicist, but also a likable celebrity. I plan to describe the lectures. For the time being, let me just enumerate them:

Lee Smolin: Loop quantum gravity: principles and phenomenology

David Spergel: What cosmological observations tell us about dark energy & inflation?

Savdeep Sethi: Matrix Big Bang

Gary Shiu: Search for realistic vacua in the landscape

Lee Smolin - LQG

I will try to minimize my comments because most readers know my opinions about LQG anyway. Lee Smolin prepared a very complete overview of loop quantum gravity. He presented the results of the work of 100+ people - one of his first transparencies contained an extensive list of 100+ LQG researchers. He also defined the symbols "R" and "S" that mean "rigorous" and "supergravity" (or more generally, "S" stands for a result that can be generalized).

Lee started with some elementary things - such as the definition of the Wilson loop. He had simplified the formula for the Wilson loop so that the astrophysicists would not be distracted by unnecessary mathematical equations. Then he claimed (...) that the LQG quantization of gauge fields works better for gravity than it does for Yang-Mills theory. He argued (...) that the background independence - whatever it exactly means - is important and realized in LQG "all the way down to the level of mathematical rigor" - a kind of phrase that appeared many times in the talk. He stated that the Hilbert space realizing some commutators (the commutator of the flux through a surface with a Wilson line is proportional to the Wilson line) is (...) unique. (You may object that the infinite-dimensional separable spaces are always isomorphic - but your objections will fail because the LQG Hilbert space is not separable.)

Thursday, May 12, 2005
... /////

This article about the Czechs, the 2005 world champions, is very acausal because it was written at different moments.

The U.S. ice-hockey national team faced the Czech Republic in Vienna during the 2005 ice-hockey world championship. The match was the exact mirror image of the same quarter final match last year in Prague. Today, the U.S. took an early 2:0 lead in the beginning. The first 60 minutes ended with a 2:2 tie. No goal occured in the following 10 minutes - overtime. The Czech Republic scored the only goal during the shootout - 3:2 is the final result.

The Czechs have won the 1998 Olympic games in Nagano much like the 1996, 1999, 2000, 2001, and 2005 world championships, see the history; the list of Czechoslovak gold medals would be too long for this blog. The Slovaks faced Canada. Although Slovakia was ahead most of the match, the Slovaks finally lost 4:5. The Canadians are simply better in dealing with the hockey sticks than the Americans; on Saturday, they will beat "unbeaten" Russia 4:3 to become the first finalist. On Sunday, Russia won the match against Sweden to grab the bronze medals.

Because the Canadians are better, it's them who faced the best ice-hockey team in the final match: the Czech Republic topped Sweden 3:2 in the other semi-final on Saturday evening - the last goal (the so-called Second Dvořák's New World Symphony) in overtime had to be confirmed by a videoreferee. What were the odds for the final match? Canada has never won a golden medal in Vienna, unlike Czechoslovakia, Czechia, the Soviet Union, and Sweden. Also, Canada has lost 1:11 with the Soviet Union in 1977 and 0:9 with Sweden in 1987 in the same city.

The previous final match between the Czech Republic and Canada took place in 1996 in Vienna, too. Canada lost 4:2 when the last two Czech goals occured within the last 19 seconds of the match. Last year, the Czechs beat Canada 6:2. The betting companies were kind of crazy because they believed that Canada's chances to win were higher than the Czech odds. However, the final match was a formality for Team Czechia. The Czechs defeated Canada 3:0.

The Czech Republic is the 2005 world champion once again. Canada deserves the silver medals, and the Russians - the only team that was able to defeat the Czechs - grabbed the bronze medals.

Last night we discussed the Ooguri-Strominger-Vafa stuff with Shiraz as the leader of the discussion. Because it's an intriguing conjecture, in comparison with other discoveries in the last year, let me describe the background for you.

Compactify type IIB on a Calabi-Yau three-fold. You obtain an N=2 theory in d=4 dimensions. It has "(h^12 + 1)" N=2 vector multiplets - the gauge fields are the Ramond-Ramond four-form contracted over "2(h^12 + 1)" existing three-cycles of the three-fold, and we erase the factor of two because the corresponding five-form field strength is self-dual.

In the vector multiplets you find scalars. These scalars are nothing else than the parameters of the complex structure - the shape of the Calabi-Yau, so to say. (The sizes of two-dimensional submanifolds are described by Kähler moduli.) You may parameterize the complex structure by the "periods" of the holomorphic three-form. What do I mean? Every Calabi-Yau space has a closed, holomorphic (3,0) form (antisymmetric tensor with three indices) called Omega, and you may integrate it over three-cycles.

To do so, it's useful to pick a good basis of the three-cycles. It is always possible to choose the cycles "A^I" and choose the following parameters to determine the complex structure:

X^I = Int(over A^I) Omega

That's nice - these periods are "(h^12 + 1)" complex parameters. There are also corresponding dual three-cycles "B_J" defined so that the intersection numbers are

#(A^I, B_J) = delta^I_J

You may want to say that the periods of "Omega" over "B_J" are new parameters of the shape, but they're not independent. They can be called "F_J":

Int(over B_J) Omega = F_J

and this "F_J" is actually always the derivative of the prepotential:

F_J = partial / partial X^J (F)

Note that the prepotential is the "N=2" generalization of the concept of the superpotential from "N=1" supersymmetric theories: it is also integrated over half of the superspace only ("d^4 theta" in this case). The prepotential is a holomorophic functions of the vector multiplets, in this case "X^I".

Several wise readers have informed me about the four Dutch theoretical physicists that have designed an experiment that will produce the light-cone gauge Green-Schwarz superstrings in your lab. Despite the authors' uncertainty what the critical dimension should be, David Goss comments that you may be able to buy a working superstring in Wal-Mart:

Patches have not been created yet; see Mozilla's announcement. The users are recommended to turn off Javascript. The Reference Frame also recommends you to use MSIE if you can - until your Firefox is patched.

Monday, May 09, 2005
... /////

The LIGO collaboration informed that the second science run did not detect any gravitational waves. The results follow from 10-day-long observations in early 2003 (two more science runs have been made ever since):

Quantitatively speaking, the number of signals at frequencies 100-1000 Hz that are shorter than 1 second and stronger than about 10^{-19} (amplitude of the metric perturbation) is smaller than 0.26 per day at 90 percent confidence level.

Some of their statistical methods to search for a signal look pretty fancy. The bounds have been improved. Only the signal is missing so far. Mother Nature is able to be as cruel as She was co-operating in the past...

Before someone is gonna blame Kip Thorne et al. for having wasted 365 million USD (the most expensive project ever funded by NSF), you should know that virtually all theoretical physicists have very good reasons to be convinced that the gravitational waves should exist, they should be visible by LIGO a bit later, and once we can detect them with some accuracy, they can tell us a lot of things about the universe.

In my previous comment "almost nothing is known about E_{11}", you may have wondered why the word "almost" appeared, and P.P. Cook has an answer.

Another small remark: on Friday Joe Marsano spoke about the symplectic structure on the phase space (space of solutions) of the half-BPS bubbling solutions asymptoting to AdS5 x S5. And it turned out he is an extraordinary speaker. Because the LLM machinery has already been described on this blog, I won't repeat Joe's excellent review of the basic picture. In calculating the symplectic 2-form - which can be written as an integral of something that can be called a symplectic current - they used the formalism of Witten and Crnkovic, among others.

Can you imagine the world without electricity, or even without Google.com? This is what some people experienced an hour ago.

If someone couldn't access Google.COM, it's because their DNS (Domain Name Server, a computer/program that translates the addresses like Google.COM to the numerical IP addresses) is down. Some people even argued that Google's domain was hijacked by SoGoSearch.COM and it showed their main screen. Others suggested that Google.COM was switching their DNS software. In the case that the problems are repeated, you can access the engine here:

Friday, May 06, 2005
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Update: an English article about the 2005 liberation festival in Pilsen. Some people doubt that there are also celebrations in other cities - those liberated by the Red Army. Let me point out that the Sunday (05/08) celebrations in Prague attracted as many as 100,000 people(English).

Sixty years ago, on May 5th, 1945, Pilsen, my Czech hometown, was liberated by the 2nd and 97th infantry divisions and the 16th armored division - soldiers led by General Patton. Most of Czechoslovakia - about 90% - was denazified by the Red Army which was one of the primary reasons why socialism controlled the country for nearly 45 years that followed. Sadly, George Patton was not allowed to take Prague.

As schoolkids, we were not taught that the U.S. troops - who were always smiling and giving chewing gums and Coke to everyone - should be credited for the victory in Pilsen. Some brave history teachers may be counted as exceptions; most teachers, however, preferred politically correct lies. Whenever a bad boy asked the question whether it was true that it was the Americans who liberated us, the teacher had to say that the only thing America did was to bomb the factories - because they already knew that we would be building socialism and they wanted to damage the emerging communist economy. Dissidents like me sometimes wanted to organize public celebrations, but it was usually difficult to figure out who could be the other participant. ;-)

Everything changed after the Velvet Revolution in 1989 - and the first celebrations of the U.S. victory in May 1990 were spectacular. Since those times, the celebrations took place every year - with a lot of military vehicles, veterans, important figures - presidents, ambassadors, Madeleine Albright, and so forth. They are just having some fun in Pilsen and the website of the 60th anniversary may be found here:

You may find some historical pictures from the end of the World War II on that web, much like newer pictures from the festivals 1990-2004. Not too many. ;-)

Thanks, General Patton, and thanks, America!

New prime minister

Just a fast comment: the Czech Republic has a new prime minister. Stanislav Gross, Europe's youngest prime minister, had to resign because of the scandal with funding a luxurious apartment (and his wife's friend's brothel), and he was replaced by another social democrat Jiří Paroubek, not to be confused with Joe Quimby, the mayor of Springfield.

Thursday, May 05, 2005
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Duiliu-Emanuel Diaconescu (Rutgers University) spoke about a generalization of the topological vertex techniques to the case of a new type of Calabi-Yau spaces that do not have to be toric: namely bundles of ruled surfaces that still admit a toric action - one that becomes degenerate not at singular points but on curves.

He conjectured a formula for the A-model topological partition sum in terms of some recursion relations describing elementary building blocks of the base of the manifold. Cumrun Vafa argued that he had the final general answer in which the recursion relations are explicitly solved, and it has not been decided yet whether Cumrun's universal ultimate answer was correct. Unfortunately the topic is too math-intensive for this blog to tell you more details.

Yuval Grossman who is with us right now - but who is otherwise affiliated with Technion and now also with Boston University - made a very good job in defending B-physics. Note that "B" stands for "bottom" or "beauty" and it is the second heaviest quark.

Why do we pay for B-physics?

Because it's the right way to test flavor physics, he argues. Well, then the next natural question is why not T-physics, C-physics, S-physics, D-physics, and U-physics. Yuval answered all these questions. For example, we do not produce too many tops so far - tens or hundreds, and it will jump by a factor of ten at the LHC. There are other problems with the charm quarks, while the u,d,s quarks are viewed as "known".

B-physics is (together with K-physics) a precision science that can be used to argue for new physics indirectly, and I will explain some numbers at the bottom of the text.

It costs a quarter to produce a B today. Another thing that Yuval had to explain is: Why do we need two B-factories instead of one? One of them is in Japan (at KEK) while the other is in California (at SLAC). The answer is that you always want to check things and replicate everything at two places. When Yuval was asked whether we also want to build two LHCs, the answer was "almost yes" - we will have two detectors (ATLAS, CMS) that will compete, and it is always a better approach to build two detectors than one better detector. Well, there will be two more detectors to be built at the LHC - ALICE and LHC-B which is gonna test B-physics.

Wednesday, May 04, 2005
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Eleven-dimensional supergravity on tori "T^k" has exceptional non-compact symmetries, and discrete subgroups of them - uniformly written as "E_{k(k)} (Z)" - are expected to be exact symmetries (U-duality groups) of the full quantum theory, namely M-theory.

For "k" smaller than 6, the exceptional symmetry can really be written as a classical symmetry. For example, for "k=5", the symmetry "E_{5(5)}(Z)" is nothing else than "SO(5,5,Z)" and this U-duality group may be seen as the T-duality group of the (1,1) little string theory - which is the BFSS-like matrix model for M-theory on "T^5" and the stringy UV completion of 5+1-dimensional Yang-Mills theory. The T-duality group of the (1,1) little string theory - which is the decoupled limit of type IIB string theory on "N" NS5-branes for the coupling at infinity going to zero - is inherited from the "big" string theory: it's the same SO(5,5,Z).

For "k=6,7,8", the U-duality group is the honest exceptional Lie group, and no proper geometric interpretation is known. For "k=9", the "E_k" group does not exist as a finite-dimensional algebra. But in a proper sense, "E_9" is nothing else than the affine "E_8". This infinite-dimensional construction is relevant for M-theory on "T^9" which has two large dimensions.

Also, Avery and Singer collected names of 500 scientists who have published papers whose content contradicts some aspects of the recent warming alarm. Sen James Inhofe has a similar list of 400+ scientists. A petition against the AGW orthodoxy was recently signed by 30,000 U.S. scientists.

Some of you may remember a paper by Naomi Oreskes in Science that claimed that 100% of the papers about global climate support the "consensus view". Well, Prof. Beiser obtained different results. And I won't try to tell you what conclusions you should make.

Since Naomi Oreskes has published her article, there have been dozens of new peer-reviewed "denier" articles about the climate. Try 10+ examples under this link where most articles are about the climate... Moreover, Madhav L. Khandekar has collected and nicely organized 60+ recent peer-reviewed articles against the global warming orthodoxy

From: Prof. Benny Peiser, Liverpool John Moores University

On December 3rd, only days before the start of the 10th Conference of Parties of the United Nations Framework Convention on Climate Change (COP-10), Science Magazine published the results of a study by Naomi Oreskes (1): For the first time, empirical evidence was presented that appeared to show an unanimous, scientific consensus on the anthropogenic causes of recent global warming.

Tuesday, May 03, 2005
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I decided to see a real physics talk - a colloquium about optics and experiments.

Kelvin Wagner from University of Colorado at Boulder was speaking about optical signal processing. While Eli Yablonovitch complained about the end of the semiconductor roadmap and the disaster that it will bring to the society, Kelvin Wagner was celebrating it.

In fact, the digital processing and electronics is a competitor of optical signal processing. The people in electronics are getting much more money, and it is only because they are cheating, Wagner was explaining: for example, they always use a fuzzy picture of the Los Angeles area obtained by optical signal processing if they want to show that their digital methods are superior.

What is optical signal processing all about? Wagner chose some old-fashioned optical computers as his first example. They were able to factorize the Mersenne number 2^{79}-1 decades ago, by a sophisticated combination of gears, holes, and light rays - this was about 1 million times faster than any other method available at that time. Well, today we have to look (digitally) for larger Mersenne numbers in order to find greater primes.

Monday, May 02, 2005
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about the representation theory of sl(2/1). However, let me mention an even more interesting paper on hep-ph. It has been exactly one month since Shelly Glashow identified the correct vacuum of string theory and completed the theory of everything. Some readers have complained that even though the abstract looked fine, the paper itself was not available - and they conjectured that the paper may be related to the date April 1st.

Sunday, May 01, 2005
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This article is mostly about the new evidence supporting global warming by Hansen et al. But let me start with an idealized energy budget of the Earth.

The average (over the surface, day, and year) energy coming from the Sun in the form of solar radiation is 342 Watts per squared meter - and almost exactly the same amount of energy is leaving the Earth. Note that 342 is exactly one quarter of the solar constant 1370 W/m^2 (the inflow of solar energy near the Earth) - it's because the radiation is only absorbed by the cross section "pi.R^2" of the planet, while we attribute it to the whole surface "4.pi.R^2" of the Earth by the averaging process.

These 342 W/m^2 may be divided in various ways - see, for example, this PDF file (which I think is, by the way, much more rational than the paper I will discuss below):

67+168+107: here, after the 342 W/m^2 approach the Earth, 67 is absorbed in the visible and UV spectrum by oxygen, ozone, and water in the atmosphere; 168 is absorbed by the surface; 107 is scattered to space in the UV and visible spectrum

107+235: here, 107 is the reflected UV and visible radiation, as explained above; 235 is the total IR radiation emitted to space; the total radiation leaving the Earth is again 342

Where do these 235 W/m^2 of "infrared" energy in the atmosphere come from?

67+66+78+24; here, 67 is the UV and visible solar radiation absorbed by the atmosphere, as mentioned above; 66 is IR radiation emitted by the surface and absorbed by the atmosphere; 78 is latent heat flux from the surface to the atmosphere (typically flowing in the rain or wet conditions); 24 is conduction and convection (from the surface to the atmosphere)

Note that the Earth's energy budget as summarized above works pretty nicely. I did not even have to consider 40 W/m^2 - a subset of those 66 W/m^2 above - which are "atmospheric windows" and may be viewed as direct IR radiation of the surface to the space.